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104
Complexity and Approximation
, 1999
"... Abstract. In this survey the following model is considered. We assume that an instance I of a computationally hard optimization problem has been solved and that we know the optimum solution of such instance. Then a new instance I ′ is proposed, obtained by means of a slight perturbation of instance ..."
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Cited by 180 (1 self)
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Abstract. In this survey the following model is considered. We assume that an instance I of a computationally hard optimization problem has been solved and that we know the optimum solution of such instance. Then a new instance I ′ is proposed, obtained by means of a slight perturbation of instance I. How can we exploit the knowledge we have on the solution of instance I to compute a (approximate) solution of instance I ′ in an efficient way? This computation model is called reoptimization and is of practical interest in various circumstances. In this article we first discuss what kind of performance we can expect for specific classes of problems and then we present some classical optimization problems (i.e. Max Knapsack, Min Steiner Tree, Scheduling) in which this approach has been fruitfully applied. Subsequently, we address vehicle routing problems and we show how the reoptimization approach can be used to obtain good approximate solution in an efficient way for some of these problems. 1
Stochastic event capture using mobile sensors subject to a quality metric
 in Proc. of ACM MobiCom
, 2006
"... Mobile sensors cover more area over a period of time than the same number of stationary sensors. However, the quality of coverage achieved by mobile sensors depends on the velocity, mobility pattern, number of mobile sensors deployed and the dynamics of the phenomenon being sensed. The gains attaine ..."
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Cited by 42 (0 self)
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Mobile sensors cover more area over a period of time than the same number of stationary sensors. However, the quality of coverage achieved by mobile sensors depends on the velocity, mobility pattern, number of mobile sensors deployed and the dynamics of the phenomenon being sensed. The gains attained by mobile sensors over static sensors and the optimal motion strategies for mobile sensors are not well understood. In this paper we consider the problem of event capture using mobile sensors. The events of interest arrive at certain points in the sensor field and fade away according to arrival and departure time distributions. An event is said to be captured if it is sensed by one of the mobile sensors before it fades away. For this scenario we analyze how the quality of coverage scales with the velocity, path and number of mobile sensors. We characterize the cases where the deployment of mobile sensors has
Improved Algorithms for Orienteering and Related Problems
, 2007
"... In this paper we consider the orienteering problem in undirected and directed graphs and obtain improved approximation algorithms. The point to pointorienteeringproblem is the following: Given an edgeweighted graph G = (V, E) (directed or undirected), two nodes s, t ∈ V and a budget B, find an st ..."
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Cited by 33 (4 self)
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In this paper we consider the orienteering problem in undirected and directed graphs and obtain improved approximation algorithms. The point to pointorienteeringproblem is the following: Given an edgeweighted graph G = (V, E) (directed or undirected), two nodes s, t ∈ V and a budget B, find an st walk in G of total length at most B that maximizes the number of distinct nodes visited by the walk. This problem is closely related to tour problems such as TSP as well as network design problems such as kMST. Our main results are the following. • A 2 + ɛ approximation in undirected graphs, improving upon the 3approximation from [5]. • An O(log 2 OPT) approximation in directed graphs. Previously, only a quasipolynomial time algorithm achieved a polylogarithmic approximation [12] (a ratio of O(log OPT)). The above results are based on, or lead to, improved algorithms for several other related problems.
An algorithmic framework for the exact solution of the prizecollecting Steiner tree problem
 Mathematical Progamming, Series B
, 2006
"... Abstract. The PrizeCollecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears frequently in the design of ut ..."
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Cited by 20 (8 self)
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Abstract. The PrizeCollecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears frequently in the design of utility networks where profit generating customers and the network connecting them have to be chosen in the most profitable way. Our main contribution is the formulation and implementation of a branchandcut algorithm based on a directed graph model where we combine several stateoftheart methods previously used for the Steiner tree problem. Our method outperforms the previously published results on the standard benchmark set of problems. We can solve all benchmark instances from the literature to optimality, including some of them for which the optimum was not known. Compared to a recent algorithm by Lucena and Resende, our new method is faster by more than two orders of magnitude. We also introduce a new class of more challenging instances and present computational results for them. Finally, for a set of largescale realworld instances arising in the design of fiber optic networks, we also obtain optimal solution values. Keywords: BranchandCut – Steiner Arborescence – Prize Collecting – Network Design 1
ZAME: Interactive Largescale Graph Visualization
"... We present the Zoomable Adjacency Matrix Explorer (ZAME), a visualization tool for exploring graphs at a scale of millions of nodes and edges. ZAME is based on an adjacency matrix graph representation aggregated at multiple scales. It allows analysts to explore a graph at many levels, zooming and p ..."
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Cited by 19 (6 self)
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We present the Zoomable Adjacency Matrix Explorer (ZAME), a visualization tool for exploring graphs at a scale of millions of nodes and edges. ZAME is based on an adjacency matrix graph representation aggregated at multiple scales. It allows analysts to explore a graph at many levels, zooming and panning with interactive performance from an overview to the most detailed views. Several components work together in the ZAME tool to make this possible. Efficient matrix ordering algorithms group related elements. Individual data cases are aggregated into higherorder metarepresentations. Aggregates are arranged into a pyramid hierarchy that allows for ondemand paging to GPU shader programs to support smooth multiscale browsing. Using ZAME, we are able to explore the entire French Wikipedia—over 500,000 articles and 6,000,000 links—with interactive performance on standard consumerlevel computer hardware.
Computing ManytoMany Shortest Paths Using Highway Hierarchies
, 2007
"... We present a fast algorithm for computing all shortest paths between source nodes s ∈ S and target nodes t ∈ T. This problem is important as an initial step for many operations research problems (e.g., the vehicle routing problem), which require the distances between S and T as input. Our approach i ..."
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Cited by 15 (5 self)
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We present a fast algorithm for computing all shortest paths between source nodes s ∈ S and target nodes t ∈ T. This problem is important as an initial step for many operations research problems (e.g., the vehicle routing problem), which require the distances between S and T as input. Our approach is based on highway hierarchies, which are also used for the currently fastest speedup techniques for shortest path queries in road networks. We show how to use highway hierarchies so that for example, a 10 000 × 10 000 distance table in the European road network can be computed in about one minute. These results are based on a simple basic idea, several refinements, and careful engineering of the approach. We also explain how the approach can be parallelized and how the computation can be restricted to computing only the k closest connections.
TSP  Infrastructure for the Traveling Salesperson Problem
 JOURNAL OF STATISTICAL SOFTWARE
, 2006
"... The traveling salesperson or salesman problem (TSP) is a well known and important combinatorial optimization problem. The goal is to find the shortest tour that visits each city in a given list exactly once and then returns to the starting city. Despite this simple problem statement, solving the TSP ..."
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Cited by 12 (2 self)
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The traveling salesperson or salesman problem (TSP) is a well known and important combinatorial optimization problem. The goal is to find the shortest tour that visits each city in a given list exactly once and then returns to the starting city. Despite this simple problem statement, solving the TSP is difficult since it belongs to the class of NPcomplete problems. The importance of the TSP arises besides from its theoretical appeal from the variety of its applications. In addition to vehicle routing, many other applications, e.g., computer wiring, cutting wallpaper, job sequencing or several data visualization techniques, require the solution of a TSP. In this paper we introduce the R package TSP which provides a basic infrastructure for handling and solving the traveling salesperson problem. The package features S3 classes for specifying a TSP and its (possibly optimal) solution as well as several heuristics to find good solutions. In addition, it provides an interface to Concorde, one of the best exact TSP solvers currently available.
Domination analysis of combinatorial optimization algorithms and problems
 In Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications (M.C. Golumbic and I. BenArroyo
, 2005
"... We provide an overview of an emerging area of domination analysis (DA) of combinatorial optimization algorithms and problems. We consider DA theory and its relevance to computational practice. 1 ..."
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Cited by 12 (7 self)
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We provide an overview of an emerging area of domination analysis (DA) of combinatorial optimization algorithms and problems. We consider DA theory and its relevance to computational practice. 1
Phase Transitions and Backbones of the Asymmetric Traveling Salesman Problem
 Journal of Artificial Intelligence Research
, 2004
"... In recent years, there has been much interest in phase transitions of combinatorial problems. ..."
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Cited by 10 (2 self)
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In recent years, there has been much interest in phase transitions of combinatorial problems.
The online asymmetric traveling salesman problem
 Proc. 9th Workshop on Algorithms and Data Structures, volume 3608 of Lecture Notes in Computer Science
, 2005
"... Abstract. We consider two online versions of the asymmetric traveling salesman problem with triangle inequality. For the homing version, in which the salesman is required to return in the city where it started from, we give a 3+√5competitive algorithm and prove that this is best 2 possible. For th ..."
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Cited by 9 (5 self)
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Abstract. We consider two online versions of the asymmetric traveling salesman problem with triangle inequality. For the homing version, in which the salesman is required to return in the city where it started from, we give a 3+√5competitive algorithm and prove that this is best 2 possible. For the nomadic version, the online analogue of the shortest asymmetric hamiltonian path problem, we show that the competitive ratio of any online algorithm depends on the amount of asymmetry of the space in which the salesman moves. We also give bounds on the competitive ratio of online algorithms that are zealous, that is, in which the salesman cannot stay idle when some city can be served. 1